Computing wrinkling and restabilization of stretched sheets based on a consistent finite-strain plate theory

Abstract

It was reported both in experiments and computations using some classical plate theories that wrinkles can appear in a uniaxially stretched rectangular hyperelastic film with clamped–clamped boundaries and can be suppressed upon further tension. Here, based on a recently-available consistent finite-strain plate theory, we investigate this complex instability problem with isola-center bifurcation (the nontrivial solution curve begins and ends at two distinct points on the trivial line) in more depth and present an efficient numerical algorithm. An advantage of this plate theory, beside its applicability to finite-strain problems, is its asymptotic consistency with the 3D field equations and surface traction conditions in a pointwise manner. Efficiency of the numerical algorithm and this consistency advantage of this plate model are examined for both Saint-Venant–Kirchhoff and incompressible neo-Hookean materials by comparing results using classical plate models. Moreover, a quantitative explanation of restabilization response is provided by exploring the difference of uniformly stretched sheets and ones with clamped–clamped boundaries. Effects of geometric and material parameters on the applicability of those classical plate models are carefully examined, and it is found that some of them may produce quantitative deviations in some situations.